Rewrite as a simplified fraction. ${0.3\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 35.5555...\\ 10x &= 3.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 32}$ ${x = \dfrac{32}{90}} $ ${x = \dfrac{16}{45}} $